Financial Modelling in Python

P1: JYS

c09 JWBK378-Fletcher May 12, 2009 19:0 Printer: Yet to come

Pricing using Numerical Methods 133

y += alphas[i]*self. fos[i](x)

return y

def fit

fos(self):

return self.

fos

class fitted

fo:

def

init (self, alphas, fo):

self.

alphas = alphas

self.

fo = fo

def

call (self, x):

return self.

fo(self. alphas, x)

The actual fitting of the approximate sum to the pickup value is carried out by the free

function fit which, in turn, delegates to the generalised least squares algorithm imple-

mented in ppf.math.generalised

least square. The free function takes in the

explanatory variables x and the values to be fitted y and returns an instance of the class

fitted

fo.

def fit(x, y):

if len(x.shape) <>2:

raise RuntimeError, "Expected ’x’ to be 2d array"

if len(y.shape) <>1:

raise RuntimeError, "Expected ’y’ to be 1d array"

num

obs = x.shape[0]

num

expl vars = x.shape[1]

if num

obs <> y.shape[0]:

raise RuntimeError, "’y’ array has wrong size"

fo=n

quadratic fo(num expl vars)

sig = numpy.zeros(num

obs)

sig.fill(1.0)

alphas = generalised

least squares fit(y, x, sig, fo.fit fos())

return fitted

fo(alphas, fo)

Given a fitted function, we need to be able to evaluate it. The free function evaluate

regression, taking in the explanatory variables x and the fitted function fo, does this for

us.

def evaluate regression(x, fo):

if len(x.shape) <>2:

raise RuntimeError, "Expected ’x’ to be a 2d array"

num

obs = x.shape[0]

y = numpy.zeros(num

obs)

for i in range(num ...